What is the difference between ∫ F∙dr and ∫ ∇f.dr, line integrals problem?

I'm trying to solve this problem

and I got the length by substituting dx by dy or the opposite, or I could use the parametric equation.
But the 2nd part is where I stop, please help me I have an exam in few hours :/ can someone explain in details how I would solve part B? Sorry for my english, not my native.
I have an exam tomorrow, please it is urgent.

and I got the length by substituting dx by dy or the opposite, or I could use the parametric equation.
But the 2nd part is where I stop, please help me I have an exam in few hours :/ can someone explain in details how I would solve part B? Sorry for my english, not my native.
I have an exam tomorrow, please it is urgent.

You are expected to know (and it is surely in your class notes and textbook) that where (c, d) are the coordinates of the end of the curve you're integrating along and (a, b) are the coordinates of the start.

And you're expected to know that if then F is conservative.

These are things you are meant to have learned long before a few hours before an exam on the subject.